5 research outputs found
A Characterization of Undirected Graphs Admitting Optimal Cost Shares
In a seminal paper, Chen, Roughgarden and Valiant studied cost sharing
protocols for network design with the objective to implement a low-cost Steiner
forest as a Nash equilibrium of an induced cost-sharing game. One of the most
intriguing open problems to date is to understand the power of budget-balanced
and separable cost sharing protocols in order to induce low-cost Steiner
forests. In this work, we focus on undirected networks and analyze topological
properties of the underlying graph so that an optimal Steiner forest can be
implemented as a Nash equilibrium (by some separable cost sharing protocol)
independent of the edge costs. We term a graph efficient if the above stated
property holds. As our main result, we give a complete characterization of
efficient undirected graphs for two-player network design games: an undirected
graph is efficient if and only if it does not contain (at least) one out of few
forbidden subgraphs. Our characterization implies that several graph classes
are efficient: generalized series-parallel graphs, fan and wheel graphs and
graphs with small cycles.Comment: 60 pages, 69 figures, OR 2017 Berlin, WINE 2017 Bangalor
Efficient black-box reductions for separable cost sharing
In cost sharing games with delays, a set of agents jointly uses a finite subset of resources. Each resource has a fixed cost that has to be shared by the players, and each agent has a non-shareable player-specific delay for each resource. A prominent example is uncapacitated facility location (UFL), where facilities need to be opened (at a shareable cost) and clients want to connect to opened facilities. Each client pays a cost share and his non-shareable physical connection cost. Given any profile of subsets used by the agents, a separable cost sharing protocol determines cost shares that satisfy budget balance on every resource and separability over the resources. Moreover, a separable protocol guarantees existence of pure Nash equilibria in the induced strategic game for the agents.
In this paper, we study separable cost sharing protocols in several general combinatorial domains. We provide black-box reductions to reduce the design of a separable cost sharing protocol to the design of an approximation algorithm for the underlying cost minimization problem. In this way, we obtain new separable cost sharing protocols in games based on arbitrary player-specific matroids, single-source connection games without delays, and connection games on n-series-parallel graphs with delays. All these reductions are efficiently computable - given an initial allocation profile, we obtain a profile of no larger cost and separable cost shares turning the profile into a pure Nash equilibrium. Hence, in these domains any approximation algorithm can be used to obtain a separable cost sharing protocol with a price of stability bounded by the approximation factor